List of top Mathematics Questions asked in KCET

The $n^{th}$ term of the series $1+3 + 7 + 13 + 21 + $ is $9901$. The value of $n$ is ................

The derivative of $e^{ax} \cos\,bx$ with respect to $x$ is $re^{ax}$ $\cos\, (bx-Tan^{-1} \frac {b}{a})$ When $a >0, b > 0$,the value of $r$ is ............

If $m$ is the slope of one of the lines represented by $ax^2 + 2hxy + by^2 = 0,$ then $(h + bm)^2$ = ______

A wire of length $20\,cm$ is bent in the form of a sector of a circle. The maximum area that can be enclosed by the wire is ____

The line joining $A (2, -7)$ and $B(6, 5)$ is divided into $4$ equal parts by the points $ P,Q$ and $R$ such that $AQ = RP = QB$. The midpoint of $ PR$ is _______

The number $(49^2 -4) (49^2 -49)$ is divisible by ..................

The constant term of the polynomial $\begin{vmatrix} {x+3}&{x} &{x+2}\\ {x}&{x+1}& {x-1} \\ {x+2}&{2x}&{3x+1}\\ \end{vmatrix} $ is ________

The order and degree of the differential equation y =$ \frac {dp}{dx}x +\sqrt {a^2p^2+b^2}$ where $ p=\frac {dy}{dx}$(here $a$ and $b$ are arbitrary constants) respectively are

Equation of the circle centered at $(4, 3)$ touching the circle $x^2+y^2-1$ externally, is _____

A simple graph contains $24$ edges. Degree of each vertex is $3$. The number of vertices is .................

If $A$ is a $3 \times 3$ nonsingular matrix and if $|A | = 3$, then $|(2A)^{-1}|$= _______

$ \displaystyle\lim _{n \rightarrow \infty} n \sin \frac{2 \pi}{3 n} \cdot \cos \frac{2 \pi}{3 n}$ is

If $y =tan ^{-1} \sqrt {x^2-1}$ then the ratio $\frac {d^2y}{dx^2}: \frac {dy}{dx}$=_________

Which of the following is NOT true?

The sides of a triangle are $6+\sqrt {12} , \sqrt {48} $ and $\sqrt {24}$. The tangent of the smallest angle of the triangle is

The locus of the point of intersection of the tangents drawn at the ends of a focal chord of the parabola $x^2=-8y$ is _______

The points $(1, 0), (0, 1), (0, 0) $ and $ (2k, 3k),k \neq 0$ are concyclic if $k$ = _____

The area bounded by the curve $ y= \begin{cases} x^2,x<0 & \quad\\ x,x \geq 0 & \quad \\ \end{cases} $ and the line $y = 4$ is

The eccentric angle of the point $(2,\sqrt{3})$ lying on $\frac {x^2}{16}+\frac{y^2}{4}-1$ is _________

If $x\neq n \pi ,\, x \neq\,(2n+1)\frac {\pi}{2}.n\in Z, $ then $\frac {Sin^{-1}(Cos x) + Cos^{-1}(Sin x)}{Tan ^{-1}(Cot x)+ Cot^{-1}(Tan x)} $ =

In $\Delta ABC$, if $a =2, B = \tan ^{-1} \frac {1}{2}$ and $C = \tan ^{-1}\frac{1}{3}$, then $(A,b)$ =

The condition for the line $y = mx +c$ to be a normal to the parabola $y = 4ax$ is _______

The set of real values of x for which $ f(x) = \frac {x}{log\, x}$ increasing, is

$P$ is the point of contact of the tangent from the origin to the curve $y = log_ex$ The length of the perpendicular drawn from the origin to the normal at $P$ is ______

The length of the diameter of the circle which cuts three circles $x^2 + y^2 - x - y - 14 = 0;$ $x^2 + y^2 + 3x - 5y - 10 = 0 ;$ $x^2 + y^2 - 2x + 3y - 27 = 0$ orthogonally, is